Relativistic solitary waves modulating long laser pulses in plasmas

TL;DR

This paper explores the existence, classification, and stability of relativistic solitary electromagnetic waves in plasmas, revealing a variety of solutions including asymmetric and multi-hump waves, with some demonstrating stability in simulations.

Contribution

It provides a comprehensive mathematical and numerical analysis of relativistic solitary waves in plasmas, including new classifications and stability assessments.

Findings

Identified a wide variety of solitary wave solutions, including asymmetric and multi-hump types.

Classified solitary waves based on grey/dark character, humps, and symmetry.

Demonstrated stability of certain grey solitary waves through particle-in-cell simulations.

Abstract

This article discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From the mathematical point of view they are exact solutions of the 1-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of traveling wave solutions with velocity $V$ and vector potential frequency $\omega$, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. By using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a great variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values, and classify them according to: (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric $V-\omega$ plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.